Question

Consider a potentiometer circuit arranged as shown in the
figure. Potentiometer wire is 600 cm long. If the jockey
touches the wire at a distance 560 cm from point A, then the
current in the galvanometer will be
B
R- 157
3E
22r
E
157
E
167
5E
22r​

Answer 1

$\frac{E}{2}$ = (15 - x)r I₁

⇒ E = 2(15 − x)r I₁ →→→(1)

E = (15−x)r I₁ + (1+x)r I₁  = 16r I₁ →→→(2)

(1) = (2)

2(15 − x) = 16

⇒ 30 − 2x = 165

⇒ x = 7

Let Jockey be places your from left,

$\bold{\therefore\frac{y}{600-y} = \frac{15-x}{x} = \frac{8}{7}}$

⇒ 7y = 4800−8y

⇒ y = $\frac{4800}{15}$

⇒ y = 320 cm

∵ 600 cm = 15r

∴ 560 cm = 14r

$\frac{E}{2}$ = 14r(I₁ + I₂) + I₂r

⇒ E = r(28I₁ + 30I₂)

⇒ E = 14r(I₁ + I₂) + 2r(I₁)

⇒ E = r(16I₁ + 14I₂)

By solving above equation,

⇒ $\heading\bold{I_2 = \frac{3E}{22r}}$

∴ $\heading\bold{I_2 = \frac{3E}{22r}}$